The richness of the iris texture and its variability across individuals make it a useful biometric trait for personal authentication. One of the key stages in classical iris recognition is the normalization process, where the annular iris region is mapped to a dimensionless pseudo-polar coordinate system. This process results in a rectangular structure that can be used to compensate for differences in scale and variations in pupil size. Most iris recognition methods in the literature adopt linear sampling in the radial and angular directions when performing iris normalization. In this paper, a biomechanical model of the iris is used to define a novel nonlinear normalization scheme that improves iris recognition accuracy under different degrees of pupil dilation. The proposed biomechanical model is used to predict the radial displacement of any point in the iris at a given dilation level, and this information is incorporated in the normalization process. Experimental results on the WVU pupil light reflex database (WVU-PLR) indicate the efficacy of the proposed technique, especially when matching iris images with large differences in pupil size.